What people used to say before smart humans invented "can't be asked" as a much more sensible replacement.

The advantage of using the phrase in question, as opposed to the aforementioned precursor, is simply one of sensibility, logic and meaning. This is evident simply from the definitions, explained thusly:

"can't be asked"

- 1 - To be incapable of fulfilling request (asking me to do this would be fruitless; implication: I am lazy / I see no point

"can't be arsed"

- 1 - I am incapable of becoming a human behind (fact, no need to be stated)

- 2 - I am incapable of becoming a fool (invariably incorrect, self-fulfilling by use of the phrase being defined)

- 3 - I am incapable of being kicked in the head by a donkey (implication: there are no donkeys in the vicinity; the arguable sole fair usage of the term provided there is indeed such a lack of equine creatures in the vicinity)

phrasee: Do this for me..
phraser: I can't be arsed.
phrasee: You're an arse. It's I can't be asked, you arse.